1. Field of the Invention
The present invention relates to Luneburg lenses and more particularly it concerns a novel Luneburg lens provided on an optical waveguide having a graded index profile, the lens having a thickness contour in accordance with the index profile of the waveguide.
2. Description of the Prior Art
A number of electro-optic and acousto-optic devices having a planar configuration have been developed for use as switches, deflectors, and RF spectrum analyzers. In these devices thin-film waveguide lenses are used for imaging, spatial filtering and focusing. The lenses for such applications should have high efficiency and high performance. Further, accuracy is essential for more precise applications where a well-collimated guided beam or sufficiently small spot size are required. Here accuracy means that the lens shape must be accurate enough to satisfy the design specifications.
A typical integrated optical lens often considered for incorporation into such devices is the Luneburg lens. S. K. Yao, et al., GUIDED-Wave Optical Thin-Film Luneburg Lenses: Fabrication Technique and Properties, App. Optics, 18,4067 (1979). This lens is fabricated by sputtering or evaporating the lens material onto the waveguide surface through a circular mask having shaped edges. The Luneburg lens has several advantages over other types of lenses for integrated device applications. First, such lenses are low in cost. This is because the appropriately made mask is repeatedly usable. Moreover, the lens materials are relatively inexpensive and only a small amount is needed for each lens. Still further, there is a wide selection of materials with a refractive index higher than that of the available waveguide materials so that one can choose the most suitable lens material for a particular purpose. In addition, fabrication is easy since it involves a conventional deposition apparatus and the thickness of the film is highly controllable although it is very important to control the lens shape since the lens characteristics are very sensitive to the film thickness and the index distribution. Finally, diffraction-limited lenses with accurately predictable focal length can be routinely made.
However, some applications, such as RF spectrum analyzers and ray scanning modules, require much more accurate focal lengths i.e. better than 1% and focal spot sizes of a few microns. Therefore, for such application, very precise Luneburg lens designs are required.
The conventional design of the Luneburg lens is based on the assumption that the waveguide thereunder is uniform and the refractive index thereof is of constant value. W. H. Southwell, Inhomogeneous Optical Waveguide Lens Analysis, J. Opt. Soc. Am., 67,1004 (1977). But in practice the method often employed for fabrication of the waveguide is thermal diffusion of a metal, such as titanium, into a substrate material of ferroelectric crystals, such as LiNbO.sub.3 or LiTaO.sub.3. Consequently, the index of the waveguide has a graded profile because the concentration of the diffused metal varies in the direction of diffusion and the index profile can be considered to follow the concentration profile. Provided that the deposited metal layer is sufficiently thin and that the concentration of diffused metal follows a simple diffusion equation, the concentration profile can be expressed as a Gaussian distribution function. Moreover, the distribution function may be changed into, for example, a simple exponential function or an Erfc function (complementary error function) in accordance with other diffusion conditions.
Thus the conventional Luneburg lens design in which a step-index profile is used as the index distribution of the waveguide does not provide sufficiently accurate results, and other lens designs must be considered in which the variation of the index profile of the waveguide is taken into account.